# Questions tagged [matrices]

For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate and adjoint, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), invariant factors, quadratic forms, etc. For questions specifically concerning matrix equations, use the (matrix-equations) tag.

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### Calculate the value of K in the matrix

If the matrix $A = \begin{pmatrix} 0 & 2 \\ K & -1 \end{pmatrix}$ satisfies $A(A^3+3I)=2I$ then value of K is: Answer: 1 Attempt: I thought of calculating polonium, and showing that the matrix ...
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### Is it possible for a nonnormal magic square to have the same magic constant as a normal magic square of the same order?

I've been programming some quick and fast solutions to 4x4 magic square problems, and I've come across an assumption I've been using: The only squares with the magic constant 34 are the normal 4x4 ...
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### Why is $(GL(2,\mathbb{Z}_3),\cdot)$ a group?

I am doing an exercise where I have to use that $(GL(2,\mathbb{Z}_3),\cdot)$ is group. I just have a hard time accepting that this a group. $GL(2,\mathbb{Z}_3)$ is described as "the set of ...
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### Matrix equation with simple solution in scalar case

I need to solve the following equation for $P \in\mathbb{R}^{r\times d}$ $$(PAP^\top)^{-1}P = G,$$ where the other quantities are known: $A\in\mathbb{R}^{d\times d}$, $G\in\mathbb{R}^{r\times d}$. If ...
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### Given an lp-norm constrain on a matrix W, I wonder the largest value of the lq-norm of W where q is the dual of p.

let $W \in \mathbb{R}^{n \times m}$ and $\Vert \cdot \Vert_p$ be the $\ell_p$-norm of a matrix, and we have $p \ge 1, \frac{1}{p} + \frac{1}{p^*} = 1$, then what is the value (or the upper bound ...
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### How to find the rotation matrix (with no x rotation) between two rotation matrices?

I need to find the rotation matrix (with no $x$ rotation) between two rotation matrices. Given a starting rotation matrix $\textbf{R}_a$ and a setpoint $\textbf{R}_{SP}$. I need to find the rotation ...
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### Bounding the operator norm of a matrix after multiplication and taking inverses.

Suppose $D$ is a $n$ by $n$ diagonal matrix with positive entries on the diagonal, and $A$ is a $m$ by $n$ matrix, is there anything we can say about the operator norm (or value of maximum entry) of ...
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Consider the map $\varphi:\text{GL}(2,\mathbb{Z}_3)\rightarrow \mathbb{Z}_3^*$, where $\varphi(M)=\text{det}(M)$ I have to show that $\varphi$ is a group homomorphism between the groups $(\text{GL}(2,... 0answers 20 views ### Characterization of representation matrix of alternating bilinear form Sorry for my bad English. Let$K$be a field s,t,${\rm ch} K=2$, and$V$be$K$-vector space of dimension$n$, and take the basis$v_1, \dots, v_n\in V$. Then bilinear form$f: V\times V\to K$is ... 0answers 43 views ### How can I find a matrix$A∈\mathbb{R}^{2\times2} $for which${A}^{3} =\begin{bmatrix} 64 & 64 \\ -9 & 16\end{bmatrix}^{-1}$? [closed] My question is to find a matrix$A∈\mathbb{R}^{2\times2}$for which $${A}^{3} =\begin{bmatrix} 64 & 64 \\ -9 & 16\end{bmatrix}^{-1}.$$ Thanks. 0answers 21 views ### Are permutation cycles equivalent to each other with respect to other permutations? Let$M$be a$0/1$matrix where$(i,i+1)$entries are$1$if$i\in\{1,\dots,n-1\}$and$(n,1)$entry is$1$and remaining entries are$0$. If$P$and$Q$are other permutation matrices when is$PMQ$... 1answer 41 views ### Finding matrix$X$with given$\cos(X)$value [closed] My question is: Find matrix$X$with given$\cos(X)$value. I tried to solve with this equation$aX+bI=\cos(X)$. with$\cos^{-1}(A)=X$but doesn't work. Find a matrix$X \in \mathbb R _ { 2 \times ...
This is a problem from Hoffman and Kunze: Let $A$, $B$, $C$, $D$ be $n \times n$ matrices over an arbitrary field $F$ that commute with each other, then the determinant of the the $2n \times 2n$ ...
Consider the determinant $$\Delta = \begin{vmatrix} x+1 & 3 & 5 \\ 2 & x+2 & 5 \\ 2 & 3 & x+4 \end{vmatrix}$$ It can be explicitly shown to be $$\Delta = (x-1)^2(x+9)$$ ...